Many models of measurement and decision-making can be characterized in terms of axioms. While it is of primary importance to test whether data are in accord to such axioms, there is a challenging incompatibility between empirical data and the nature of the axioms. On the one hand, empirical data generally contain random error, which is attributable to a number of sources, such as the inherent unreliability of human (or animal) behavior, sampling error, and imprecision of the observations themselves. On the other hand, the axioms do not account for random error, because of their deterministic, qualitative form. This research project aims to solve this incompatibility by developing procedures of axiom testing that are based on contemporary Bayesian methods of model estimation, model fit evaluation, and model selection. Through five inter-related research objectives, this project will investigate the Bayes inference framework by applying it to test axioms on real data, and by comparing the performance of different types of model selection methods and prior distributions. The goal is to determine the best Bayesian inference methods for testing axioms of measurement.
For researchers in many branches of the social sciences, including test theory and decision theory, the fruits of this work should provide usable and powerful statistical tools for testing the key assumptions that underlies contemporary models of measurement and decision-making. The use of these statistical tools should lead to a better understanding of these models, and possibly indicate productive extensions of them.
